You asked what time it is, so I am going to tell you how to build a watch...

Headlight descriptions can be confusing, mostly thanks to the lying sales weasels.

"Standard" - virtually obsolete. Tungsten filament inside a separate small bulb, or inside the large glass bulb. The sales weasels called the large units "sealed beam" headlamps when they were introduced way back when.

"Halogen" - small bulb made of fused quartz or similar material, with a halogen gas surrounding the filament. The sales weasels called these "quartz-iodide" at first, then "quartz-halogen" when gases other than iodine were used, and now just called "halogen" - except when the weasels want to make them sound new and exciting. Then they call them "xenon". Xenon is just another gas used in the quartz/tungsten bulbs. A (very) little bit better than the usual halogen gases.

"Xenon" - At one point, referred to a new type of bulb. This had no filament, but fired an arc thru xenon gas to create a hotter (thus whiter, then bluer) light. More efficient - more light per watt of power used. Whiter light.

The lying sales weasels (not all sales weasels are lying sales weasels - just the 90% who give the rest of them a bad name) immediately introduced quartz-halogen bulbs with xenon gas and a dicrotic filter coating that gave a bluer light and called them "xenon" bulbs. The boy racers jumped all over them, either not knowing or not caring that making bluer light from a normal tungsten filament can only be done by removing the red portion of the light, so you can't see at night worth a damn...

The xenon arc lamps are now beginning to be called "H.I.D." (High Intensity Discharge) lamps. They require a "ballast" to work, and also will not work well in a reflector/lens unit designed for tungsten-filament (standard, halogen or xenon) bulbs.

In your case, the vendor is saying that the lights will not work with true xenon, or H.I.D. bulbs. They should work fine with halogen bulbs, or the "xenon" bulbs that are really just tungsten-filament bulbs with a little xenon gas.

And, just to add yet more verbiage to a long post...
Halogen bulbs give brighter, whiter light than normal tungsten bulbs. They do this by being overdriven - that is, using a filament that would normally be suitable for a 6-volt system and driving it with 12 volts. This works because surrounding the tungsten filament with a halogen gas (or xenon), changes the way the filament burns.

In a normal tungsten bulb (car or home), the tungsten gets hot enough to glow. If there is a tiny flaw in the filament, that spot will burn a little hotter. The tungsten evaporates just a little faster from the hotter spot, which makes it thinner. That makes that spot hotter, so more tungsten evaporates, which makes it hotter, so more tungsten evaporates... Poof!

If you surround the filament with the proper gases, things change. The gases make the evaporated tungsten redeposit onto the filament, and the tungsten deposits better as the filament gets hotter. So, a hot spot gets more tungsten deposited, and gets thicker instead of weaker. This makes the tungsten "self-healing" in effect, so you can over-drive the filament, and still get reasonable life out of it.

<lecture mode off>

The odds are that you have halogen headlights, so your new ones should be fine. You would know if you had H.I.D. lights.